Shuch first learned about SETI, the electromagnetic Search for ExtraTerrestrial Intelligence, from Nicholas Marshall, W6OLO, a Hungarian engineer with whom he served on the Board of Project OSCAR, builders of the world's first non-Government satellite. Marshall introduced Shuch to longtime SETI proponent Dr. Bernard M. "Barney" Oliver, then vice-president of Engineering at the Hewlett-Packard Company. Oliver in turn introduced Paul to SETI pioneers Frank Drake and Philip Morrison, who encouraged his continued interest and involvement in the development of SETI radio telescopes, as a spin-off from his design of early satellite TV receivers.

While in graduate school at the University of California, Berkeley, Shuch became acquainted with most of the members of the NASA SETI team in nearby Mountain View, CA. Many SETI pioneers had been affiliated with Berkeley, either as faculty members, students, or postdoctoral researchers, and a SETI-friendly environment (some have called it a 'SETI cabal') persists there. Among Shuch's professors was the prominent radio astronomer William J. "Jack" Welch, a member of the National Academy of Science, who further encouraged Shuch's SETI activities. One of Shuch's classmates in Welch's radio telescope design course was Dan Werthimer, who went on to become chief scientist of the SETI@home distributed computing experiment.

When the NASA SETI program was cancelled by the US Congress in 1993, New Jersey industrialist Richard Factor established the nonprofit, membership-supported SETI League,[5] which he invited Shuch to head. Shuch became the organization's first Executive Director,[6] a position he now holds on an emeritus basis. He designed the hardware and protocols for, and remains Principal Investigator on, the SETI League's Project Argus [3] all-sky survey[7][8][9]

Shuch is principal investigator for the Invitation to ETI [10][4], a web-based SETI experiment initiated by his colleague, Allen Tough. Along with Ivan Almar of the Konkoly Observatory, Budapest, Shuch developed the San Marino Scale[5],[11] an analytical tool for quantifying the significance of transmissions from Earth into Space.[12]